Shun-ichi Kitahara

Perfect monopole action for infrared SU(2) QCD

Abstract Performing block-spin transformations on the dual lattice after abelian projection, we obtain an almost perfect lattice action in terms of monopole currents in the infrared region of pure SU (2) QCD. The action depends only on a physical scale b and is free from a cut-off a ( β ). It reproduces analytically the string tension which is near the physical one for a wide physical-scale region (b ⩾ 1.0(κ −1 2 )) .

Deconfinement transition and monopoles in T does not = 0 SU(2) QCD

The role of monopoles in the deconfinement transition is discussed in the framework of abelian projection in the maximally abelian gauge in T=I=O SU(2) QCD. Only one (or a few near flc) long connected monopole loop exists uniformly through the whole lattice in each vacuum configuration in addition to some very short loops in the confinement phase and the long loop disappears in the deep deconfinement region. Energy·entropy balance of the long loops of maximally extended monopoles explains the existence of the deconfinement transition and reproduces roughly the value of the critical temperature.

Monopole action and monopole condensation in SU(3) lattice QCD

Abstract Effective monopole actions for various extended monopoles are derived from vacuum configurations after abelian projection in the maximally abelian gauge in T = 0 and T ≠ 0 SU(3) lattice QCD. The actions obtained appear to be independent of the lattice volume adopted. At zero temperature, monopole condensation is seen to occur from energy-entropy balance in the strong coupling region. Larger β is included in the monopole condensed phase as more extended monopoles are considered. The scaling seen in the SU(2) case is not yet observed. The renormalization flow diagram suggests the existence of an infrared fixed point. A hysteresis behavior is seen around the critical temperature in the case of the T ≠ 0 action.

Three topics of monopole dynamics in abelian projected QCD

Abstract Three topics about monopole dynamics after abelian projection are reported. The first is the new and detailed analyses of SU (2) monopole action obtained after the block-spin transformation on the dual lattice. The b = na (β) dependence for all couplings are well fitted with a universal curve. The distance dependence of the couplings is well reproduced by a massive propagator with the mass m = 0.8 in unit of b . The second is the SU (3) monopole action recently obtained. The third is new interesting gauges showing abelian and monopole dominances as in the maximally abelian gauge.

Disorder parameter of confinement

Abstract The disorder parameter of confinement-deconfinement phase transition based on the monopole action determined previously in SU(2) QCD are investigated. We construct an operator which corresponds to the order parameter defined in the abelian Higgs model. The operator shows proper behaviors as the disorder parameter in the numerical simulations of finite temperature QCD.

Critical exponents and abelian dominance in SU(2) QCD

Abstract The critical properties of the abelian Polyakov loop and the Polyakov loop in terms of Dirac string are studied in finite temperature abelian projected SU (2) QCD. We evaluate the critical point and the critical exponents from each Polyakov loop in the maximally abelian gauge using the finite-size scaling analysis. Abelian dominance in this case is proved quantitatively. The critical point of each abelian Polyakov loop is equal to that of the non-abelian Polyakov loop within the statistical errors. Also, the critical exponents are in good agreement with those from non-abelian Polyakov loops.

Monopoles and hadron spectrum in quenched QCD

Abstract We study quenched hadron spectra with Wilson fermions in abelian gauge fields extracted by maximal abelian projection and in fields induced by monopoles on 16 3 × 32 and 12 3 × 24 lattices. The pion mass squared and the quark mass defined through the axial Ward identity satisfy the PCAC relation. Gross features of the light hadron spectra are almost similar to those in SU (3) gauge fields if normalization is done by the square root of the string tension. It is also shown that no sizable dynamical mass generation is found in the present range of κ when the monopole degree of freedom is removed from the abelian fields or from the SU (3) gauge fields.

Lattice monopole action in pure SU(3) QCD

We obtain an almost perfect monopole action numerically after abelian projection in pure SU(3) lattice QCD. Performing block-spin transformations on the dual lattice, the action fixed depends only on a physical scale b. Monopole condensation occurs for large b region. The numerical results show that two-point monopole interactions are dominant for large b. We next perform the block-spin transformation analytically in a simplified case of two-point monopole interactions with a Wilson loop on the fine lattice. The perfect operator evaluating the static quark potential on the coarse b-lattice are derived. The monopole partition function can be transformed into that of the string model. The static potential and the string tension are estimated in the string model framework. The rotational invariance of the static potential is recovered, but the string tension is a little larger than the physical one.We obtain an almost perfect monopole action numerically after abelian projection in pure SU(3) lattice QCD. Performing block-spin transformations on the dual lattice, the action fixed depends only on a physical scale b. Monopole condensation occurs for large b region. The numerical results show that two-point monopole interactions are dominant for large b. We next perform the block-spin transformation analytically in a simplified case of two-point monopole interactions with a Wilson loop on the fine lattice. The perfect operator evaluating the static quark potential on the coarse b-lattice are derived. The monopole partition function can be transformed into that of the string model. The static potential and the string tension are estimated in the string model framework. The rotational invariance of the static potential is recovered, but the string tension is a little larger than the physical one.

Various representations of infrared effective lattice QCD

Abstract We study various representations of the infrared effective theory of SU(2) gluodynamics starting from the monopole action derived recently. We determine the coupling constants in the abelian-Higgs model directly from lattice QCD and evaluate the type of the QCD vacuum. The string action is derived using the BKT transformation on the lattice. At the classical level this action reproduces the physical string tension with a good accuracy.

Gauge problem of monopole dynamics in SU(2) lattice gauge theory

Gauge problem of monopole dynamics is studied in SU(2) lattice gauge theory. We study first abelian and monopole contributions to the static potential in four smooth gauges, i.e., Laplacian Abelian (LA), Maximally Abelian Wilson Loop (MAWL) and L-type gauges in comparison with Maximally Abelian (MA) gauge. They all reproduce the string tension in good agreement with the SU(2) string tension. MA gauge is not the only choice of the good gauge which is suitable for the color confinement mechanism. Using an inverse Monte-Carlo method and the blockspin transformation, we determine effective monopole actions and the renormalization group (RG) flows of its coupling constants in various abelian projection schemes. Every RG flow looks to converge to a unique curve which suggests gauge independence in the infrared region.